Finite Group Databasebeta

← #13079088

Subgroups — #13079088

Order 1408.

564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#535C211yesmaximal, characteristic, complemented
2C2×#67004C211yesmaximal, characteristic, complemented
3C2×#67003C211yesmaximal, characteristic, complemented
4C22×#4324C211yesmaximal, characteristic, complemented
5C2×#66985C211yesmaximal, characteristic, complemented
6#10623057C211yesmaximal, characteristic, complemented
7#10622689C212yesmaximal, complemented
8#10622687C212yesmaximal, complemented
9#10622673C212yesmaximal, complemented
10#10622672C212yesmaximal, complemented
11#10622610C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×D4×C11C2211yescharacteristic
14C2×#4339C2211yescharacteristic
15C22×Dic22C2211yescharacteristic
16C11×#127C2212yes—
17C11×#124C2212yes—
18C11×#121—22no—
19C11×#120—22no—
20C11×#117C2211yescharacteristic
21#67004—24no—
22#67003—24no—
23C2×#4326C2211yescharacteristic, complemented
24C2×#4326C2212yescomplemented
25C2×#4325C2211yescharacteristic, complemented
26C2×#4324—24no—
27C2×#4324C2212yes—
28C2×#4324C2212yes—
29C2×#4324C2212yes—
30C2×#4324C2211yescharacteristic, complemented
31C2×#4324C2212yescomplemented
32#66985—24no—
33C2×#4323C2212yes—
34C2×#4323C2211yescharacteristic, complemented
35C2×#4318C2211yescharacteristic
36C22×C11⋊C8C2211yescharacteristic
37#66950—22no—
38#66939—22no—
39#66928C2212yescomplemented
40#66922C2212yescomplemented
41#66867C2212yescomplemented
42C4×C11⋊C8C2212yescomplemented
43C24×C11—21no—
44C11×#41—22no—
45C11×#41—22no—
46C2×Q8×C11C2311yescharacteristic
47C2×D4×C11—21no—
48C2×D4×C11—22no—
49C2×D4×C11—22no—
50C2×D4×C11—21no—
51C2×D4×C11—24no—
52C2×D4×C11C2312yes—
53C2×D4×C11C2311yescharacteristic
54C22×C4×C11—21no—
55C22×C4×C11C2311yescharacteristic
56C2×C22⋊D11—21no—
57C22×Dic11—21no—
58#4339—22no—
59#4339—22no—
60C2×D44C2311yescharacteristic
61C2×C4×D11—21no—
62C2×Dic22—22no—
63C2×Dic22—22no—
64C2×Dic22—21no—
65C2×Dic22C2311yescharacteristic
66C2×Dic22C2312yes—
67C11×C4⋊C4D412yes—
68C11×C22⋊C4—24no—
69C11×C22⋊C4D412yes—
70C42×C11C2312yes—
71#4326—22no—
72#4326—24no—
73#4325—22no—
74#4324—24no—
75#4324—24no—
76#4324—24no—
77#4324—22no—
78#4324—24no—
79#4323—24no—
80#4323—22no—
81(C2×D11)⋊C4—24no—
82C4⋊Dic11—24no—
83#4318D414yescomplemented
84C2×C11⋊C8D414yescomplemented
85C2×C11⋊C8C2311yescharacteristic
86C2×C11⋊C8C2312yes—
87C2×C11⋊C8C2311yescharacteristic
88#3154—111nomaximal, Sylow
89C23×C11—22no—
90C23×C11—21no—
91C23×C11—42no—
92C23×C11—82no—
93C23×C11C2×D411yescharacteristic
94C22×D11—21no—
95Q8×C11—21no—
96Q8×C11—21no—
97D4×C11—22no—
98D4×C11—21no—
99D4×C11—22no—
100D4×C11—21no—
101D4×C11—42no—
102D4×C11—42no—
103D4×C11—84no—
104C2×C4×C11—21no—
105C2×C4×C11—42no—
106C2×C4×C11C2×D412yes—
107C2×C4×C11C2×D412yes—
108C2×C4×C11C2×D414yes—
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2411yescharacteristic
111C22⋊D11—42no—
112C2×Dic11—21no—
113C2×Dic11—22no—
114C2×Dic11—42no—
115D44—21no—
116D44—21no—
117C4×D11—42no—
118Dic22—22no—
119Dic22—21no—
120Dic22—22no—
121Dic22—21no—
122Dic22—42no—
123C11⋊C8C2×D412yes—
124C11⋊C8C2×D412yes—
125C11⋊C8C2×D414yes—
126C2×#137—111no—
127C2×AGL(1,ℤ/8)—111no—
128C2×#135—111no—
129C22×SD16—111no—
130#536—111no—
131#535D1111yescharacteristic, complemented
132#497—112no—
133#496—112no—
134#495—112no—
135#492—112no—
136#405—111no—
137C22×C11—22no—
138C22×C11—41no—
139C22×C11—42no—
140C22×C11—42no—
141C22×C11—44no—
142C22×C11—84no—
143C22×C11#12712yes—
144C22×C11C22×D411yescharacteristic
145C2×D11—41no—
146C2×D11—42no—
147C4×C11—24no—
148C4×C11—41no—
149C4×C11#12712yes—
150C4×C11C22×D411yescharacteristic
151C4×C11C22×D411yescharacteristic
152Dic11—42no—
153Dic11—41no—
154C2×#41—111no—
155C2×#41C2×D1111yescharacteristic
156C22×Q8—111no—
157C22×D4C2×D1111yescharacteristic
158#137—224no—
159AGL(1,ℤ/8)—224no—
160#135—224no—
161C2×Q16—111no—
162C2×Q16—112no—
163C2×SD16—111no—
164C2×SD16—112no—
165C2×SD16—112no—
166C2×SD16—111no—
167C2×SD16—112no—
168C2×SD16—112no—
169C2×SD16—224no—
170C2×D8—111no—
171C2×D8—112no—
172C2×M16—111no—
173C22×C8—111no—
174C4⋊Q8—112no—
175#127C2×D1112yes—
176#124—112no—
177#124C2×D1112yes—
178#123—222no—
179C22⋊Q8—222no—
180#121—22no—
181#120—22no—
182#117C2×D1111yescharacteristic
183#97—112no—
184C4×C8—112no—
185C2×C11—22no—
186C2×C11—81no—
187C2×C11—82no—
188C2×C11C2×#12711yescharacteristic
189C2×C11#57712yes—
190D11—81no—
191C24—21no—
192#41—22no—
193#41—22no—
194#41—222no—
195#41—222no—
196C2×Q8—112no—
197C2×Q8—111no—
198C2×Q8—221no—
199C2×Q8—222no—
200C2×Q8—222no—
201C2×Q8C22×D1111yescharacteristic
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—22no—
205C2×D4—21no—
206C2×D4—24no—
207C2×D4—111no—
208C2×D4—221no—
209C2×D4C22×D1112yes—
210C2×D4C22×D1111yescharacteristic
211C22×C4—21no—
212C22×C4—221no—
213C22×C4—221no—
214C22×C4C22×D1111yescharacteristic
215Q16—222no—
216Q16—224no—
217SD16—224no—
218SD16—224no—
219SD16—222no—
220SD16—224no—
221SD16—224no—
222SD16—222no—
223D8—222no—
224D8—224no—
225M16—114no—
226C2×C8—114no—
227C2×C8—111no—
228C2×C8—112no—
229C2×C8—111no—
230C4⋊C4—224no—
231C4⋊C4C22⋊D1112yes—
232C22⋊C4—24no—
233C22⋊C4—224no—
234C22⋊C4C22⋊D1112yes—
235C42C22×D1112yes—
236C11#315411yescharacteristic, complemented, Sylow
237C23—22no—
238C23—21no—
239C23—42no—
240C23—82no—
241C23—221no—
242C23C2×C22⋊D1111yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—222no—
246Q8—221no—
247Q8—222no—
248Q8—221no—
249Q8—442no—
250D4—22no—
251D4—21no—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—84no—
257D4—221no—
258D4—221no—
259D4—442no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—222no—
263C2×C4—221no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4D4×D1112yes—
267C2×C4D4×D1112yes—
268C2×C4C2×C22⋊D1114yes—
269C2×C4C2×C22⋊D1111yescharacteristic
270C2×C4C23×D1111yescharacteristic
271C8—112no—
272C8—112no—
273C8—114no—
274C22—22no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—44no—
279C22—84no—
280C22—441no—
281C22—442no—
282C22#6699312yes—
283C22C22×C22⋊D1111yescharacteristic
284C4—24no—
285C4—41no—
286C4—441no—
287C4—442no—
288C4#6699312yes—
289C4C2×D4×D1111yescharacteristic
290C4C2×D4×D1111yescharacteristic
291C2—22no—
292C2—82no—
293C2—81no—
294C2—881no—
295C2C2×#6699311yescharacteristic
296C2#1062336712yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#535C2
socleC22×C11C22×D4
hypercenter#535D11
hypocenterC11#3154
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#535C2semidirect
2. C2×#67004C2semidirect
3. C2×#67003C2semidirect
4. C22×#4324C2semidirect
5. C2×#66985C2semidirect
6. #10623057C2semidirect
7. #10622689C2semidirect
8. #10622687C2semidirect
9. #10622673C2semidirect
10. #10622672C2semidirect
11. #10622610C2semidirect
23. C2×#4326C22semidirect
24. C2×#4326C22semidirect
25. C2×#4325C22semidirect
30. C2×#4324C22semidirect
31. C2×#4324C22semidirect
34. C2×#4323C22semidirect
39. #66928C22semidirect
40. #66922C22semidirect
41. #66867C22semidirect
42. C4×C11⋊C8C22semidirect
83. #4318D4semidirect
84. C2×C11⋊C8D4semidirect
131. #535D11semidirect
236. C11#3154semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#5352
C2×#670042
C2×#670032
C22×#43242
C2×#669852
#106230572
#106226892
#106226872
#106226732
#106226722
#106226102
#315411